| author | Christian Urban <christian.urban@kcl.ac.uk> |
| Thu, 11 Nov 2021 15:58:22 +0000 | |
| changeset 849 | 3d5ecb8f1f2f |
| parent 809 | 2b9956d29038 |
| child 871 | 94b84d880c2b |
| permissions | -rw-r--r-- |
| 666 | 1 |
% !TEX program = xelatex |
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\documentclass[dvipsnames,14pt,t,xelatex,aspectratio=169,xcolor={table}]{beamer}
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\usepackage{../slides}
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\usepackage{../graphics}
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\usepackage{../langs}
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\usepackage{../data}
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\usepackage{../grammar}
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% beamer stuff |
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\renewcommand{\slidecaption}{CFL 06, King's College London}
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\newcommand{\bl}[1]{\textcolor{blue}{#1}}
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%\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
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\newcommand{\qq}{\mbox{\texttt{"}}}
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\usepackage{tcolorbox}
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\newtcolorbox{mybox}{colback=red!5!white,colframe=red!75!black}
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\newtcolorbox{mybox2}[1]{colback=red!5!white,colframe=red!75!black,fonttitle=\bfseries,title=#1}
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\newtcolorbox{mybox3}[1]{colback=Cyan!5!white,colframe=Cyan!75!black,fonttitle=\bfseries,title=#1}
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[t]
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\frametitle{%
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\begin{tabular}{@ {}c@ {}}
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\\[-3mm] |
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\LARGE Compilers and \\[-2mm] |
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\LARGE Formal Languages\\[3mm] |
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\end{tabular}}
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\normalsize |
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\begin{center}
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\begin{tabular}{ll}
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Email: & christian.urban at kcl.ac.uk\\ |
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%Office Hours: & Thursdays 12 -- 14\\ |
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%Location: & N7.07 (North Wing, Bush House)\\ |
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Slides \& Progs: & KEATS (also homework is there)\\ |
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\end{tabular}
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\end{center}
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\begin{center}
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\begin{tikzpicture}
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\node[drop shadow,fill=white,inner sep=0pt] |
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{\footnotesize\rowcolors{1}{capri!10}{white}
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\begin{tabular}{|p{4.8cm}|p{4.8cm}|}\hline
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1 Introduction, Languages & \cellcolor{blue!50} 6 While-Language \\
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2 Regular Expressions, Derivatives & 7 Compilation, JVM \\ |
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3 Automata, Regular Languages & 8 Compiling Functional Languages \\ |
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4 Lexing, Tokenising & 9 Optimisations \\ |
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5 Grammars, Parsing & 10 LLVM \\ \hline |
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\end{tabular}%
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}; |
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\end{tikzpicture}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Parser Combinators}
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One of the simplest ways to implement a parser, see |
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{\small\url{https://vimeo.com/142341803}} (by Haoyi Li)\bigskip
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\begin{itemize}
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\item[$\bullet$] build-in library in Scala |
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\item[$\bullet$] fastparse (2) library by Haoyi Li; is part of Ammonite |
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\item[$\bullet$] possible exponential runtime behaviour |
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Parser Combinators}
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Parser combinators: \bigskip |
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\begin{minipage}{1.1\textwidth}
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\begin{center}
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\mbox{}\hspace{-12mm}\mbox{}$\underbrace{\text{list of tokens}}_{\text{input}}$ \bl{$\Rightarrow$}
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$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
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\end{center}
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\end{minipage}\bigskip
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\begin{itemize}
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\item atomic parsers |
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\item sequencing |
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\item alternative |
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\item semantic action (map-parser) |
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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Atomic parsers, for example, number tokens |
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\begin{center}
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\bl{$\texttt{Num(123)}::rest \;\Rightarrow\; \{(\texttt{Num(123)}, rest)\}$}
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\end{center}\bigskip
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\begin{itemize}
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\item you consume one or more token from the\\ |
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input (stream) |
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\item also works for characters and strings |
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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Alternative parser (code \bl{$p\;||\;q$})\bigskip
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\begin{itemize}
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\item apply \bl{$p$} and also \bl{$q$}; then combine
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the outputs |
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\end{itemize}
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\begin{center}
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\large \bl{$p(\text{input}) \cup q(\text{input})$}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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Sequence parser (code \bl{$p\sim q$})\bigskip
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\begin{itemize}
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\item apply first \bl{$p$} producing a set of pairs
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\item then apply \bl{$q$} to the unparsed parts
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\item then combine the results:\medskip |
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\begin{center}
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((output$_1$, output$_2$), unparsed part) |
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\end{center}
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\end{itemize}
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\begin{center}
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\begin{tabular}{l}
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\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
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\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
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\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
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\end{tabular}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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Map-parser (code \bl{$p.map(f)\;$})\bigskip
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\begin{itemize}
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\item apply \bl{$p$} producing a set of pairs
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\item then apply the function \bl{$f$} to each first component
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\end{itemize}
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\begin{center}
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\begin{tabular}{l}
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\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
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\end{tabular}
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\end{center}\bigskip\bigskip\pause
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\bl{$f$} is the semantic action (``what to do with the parsed input'')
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
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Addition |
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\begin{center}
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\bl{$\meta{T} \sim + \sim \meta{E} \Rightarrow \underbrace{f\,((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
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\end{center}\pause
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Multiplication |
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\begin{center}
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\bl{$\meta{F} \sim * \sim \meta{T} \Rightarrow f\,((x,y), z) \Rightarrow x * z$}
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\end{center}\pause
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Parenthesis |
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\begin{center}
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\bl{$\text{(} \sim \meta{E} \sim \text{)} \Rightarrow f\,((x,y), z) \Rightarrow y$}
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\end{center}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Input Types of Parsers}
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\begin{itemize}
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\item input: \alert{token list}
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\item output: set of (output\_type, \alert{token list})
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\end{itemize}\bigskip\pause
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actually it can be any input type as long as it is a kind of |
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sequence (for example a string) |
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Scannerless Parsers}
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\begin{itemize}
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\item input: \alert{string}
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\item output: set of (output\_type, \alert{string})
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\end{itemize}\bigskip\bigskip
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but using lexers is better because whitespaces or comments can be |
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filtered out; then input is a sequence of tokens |
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Abstract Parser Class}
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\small |
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\lstinputlisting[language=Scala,xleftmargin=1mm] |
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{../progs/app7.scala}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{Successful Parses}
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\begin{itemize}
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\item input: string |
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\item output: \alert{set of} (output\_type, string)
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\end{itemize}\bigskip
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a parse is successful whenever the input has been fully |
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``consumed'' (that is the second component is empty) |
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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%%\frametitle{Test Program}
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\mbox{}\\[-18mm]\mbox{}
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{\lstset{language=While}%%\fontsize{10}{12}\selectfont
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\texttt{\lstinputlisting{../progs/while-tests/loops.while}}}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}
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\frametitle{While-Language}
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\mbox{}\\[-23mm]\mbox{}
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\bl{\begin{plstx}[rhs style=,one per line]: \meta{Stmt} ::= skip
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| \meta{Id} := \meta{AExp}
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| if \meta{BExp} then \meta{Block} else \meta{Block}
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| while \meta{BExp} do \meta{Block}\\
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: \meta{Stmts} ::= \meta{Stmt} ; \meta{Stmts}
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| \meta{Stmt}\\
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: \meta{Block} ::= \{ \meta{Stmts} \}
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| \meta{Stmt}\\
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: \meta{AExp} ::= \ldots\\
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: \meta{BExp} ::= \ldots\\\end{plstx}}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Aexps\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{@{}lcl@{}}
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$\text{eval}(n)$ & $\dn$ & $n$\\
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$\text{eval}(a_1 + a_2)$ & $\dn$ & $\text{eval}(a_1) + \text{eval}(a_2)$\\
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$\text{eval}(a_1 - a_2)$ & $\dn$ & $\text{eval}(a_1) - \text{eval}(a_2)$\\
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$\text{eval}(a_1 * a_2)$ & $\dn$ & $\text{eval}(a_1) * \text{eval}(a_2)$\bigskip\\
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$\text{eval}(x)$ & $\dn$ & $???$\\
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\end{tabular}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Interpreter\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{@{}lcl@{}}
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$\text{eval}(n, E)$ & $\dn$ & $n$\\
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$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
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$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
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$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
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$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
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$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
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$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
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$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
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\end{tabular}}
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\end{center}
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\end{frame}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{frame}[c]
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\frametitle{An Interpreter (1)}
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\begin{center}
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\bl{\begin{tabular}{l}
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$\{$\\
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\;\;$x := 5 \text{;}$\\
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\;\;$y := x * 3\text{;}$\\
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\;\;$y := x * 4\text{;}$\\
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\;\;$x := u * 3$\\ |
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$\}$ |
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\end{tabular}}
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\end{center}
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\begin{itemize}
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\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
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\item \bl{\texttt{eval(stmt, env)}}
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\end{itemize}
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\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\mode<presentation>{
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\begin{frame}[c]
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\frametitle{\begin{tabular}{c}Interpreter (2)\end{tabular}}
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\begin{center}
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\bl{\begin{tabular}{@{}lcl@{}}
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$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
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$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
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\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
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\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
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\text{eval}(cs_1,E)$}\\
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\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
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\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
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\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
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\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
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\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
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\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
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$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
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\end{tabular}}
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|
386 |
\end{center}
|
|
387 |
||
388 |
\end{frame}}
|
|
389 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
390 |
||
391 |
||
392 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
393 |
\mode<presentation>{
|
|
394 |
\begin{frame}[t]
|
|
395 |
\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
|
|
396 |
||
397 |
\begin{center}
|
|
398 |
\begin{tikzpicture}
|
|
399 |
\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
|
|
400 |
\addplot+[smooth] file {interpreted.data};
|
|
401 |
\end{axis}
|
|
402 |
\end{tikzpicture}
|
|
403 |
\end{center}
|
|
404 |
||
405 |
\end{frame}}
|
|
406 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
407 |
||
| 809 | 408 |
|
409 |
\begin{frame}[t,fragile]
|
|
410 |
\begin{mybox3}{}
|
|
411 |
In CW3, in the collatz program there is the line write "$\backslash$n" Should this print "/n" or perform the new line command /n ? Also should write be print() or println() ? |
|
412 |
\end{mybox3}
|
|
413 |
\end{frame}
|
|
414 |
||
415 |
||
| 849 | 416 |
\begin{frame}<1-20>[c]
|
| 809 | 417 |
\end{frame}
|
418 |
||
419 |
||
| 803 | 420 |
\end{document}
|
421 |
||
422 |
||
| 799 | 423 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
424 |
\mode<presentation>{
|
|
425 |
\begin{frame}[c]
|
|
426 |
\frametitle{\begin{tabular}{c}Java Virtual Machine\end{tabular}}
|
|
427 |
||
428 |
\begin{itemize}
|
|
429 |
\item introduced in 1995 |
|
430 |
\item is a stack-based VM (like Postscript, CLR of .Net) |
|
431 |
\item contains a JIT compiler |
|
432 |
\item many languages take advantage of JVM's infrastructure (JRE) |
|
433 |
\item is garbage collected $\Rightarrow$ no buffer overflows |
|
434 |
\item some languages compile to the JVM: Scala, Clojure\ldots |
|
435 |
\end{itemize}
|
|
436 |
||
437 |
\end{frame}}
|
|
438 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
439 |
||
440 |
||
441 |
||
| 803 | 442 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
443 |
% \begin{frame}[t]
|
|
444 |
% \frametitle{%
|
|
445 |
% \begin{tabular}{@ {}c@ {}}
|
|
446 |
% \\[-3mm] |
|
447 |
% \LARGE Compilers and \\[-2mm] |
|
448 |
% \LARGE Formal Languages\\[3mm] |
|
449 |
% \end{tabular}}
|
|
| 799 | 450 |
|
| 803 | 451 |
% \normalsize |
452 |
% \begin{center}
|
|
453 |
% \begin{tabular}{ll}
|
|
454 |
% Email: & christian.urban at kcl.ac.uk\\ |
|
455 |
% %Office Hours: & Thursdays 12 -- 14\\ |
|
456 |
% %Location: & N7.07 (North Wing, Bush House)\\ |
|
457 |
% Slides \& Progs: & KEATS (also homework is there)\\ |
|
458 |
% \end{tabular}
|
|
459 |
% \end{center}
|
|
| 799 | 460 |
|
| 803 | 461 |
% \begin{center}
|
462 |
% \begin{tikzpicture}
|
|
463 |
% \node[drop shadow,fill=white,inner sep=0pt] |
|
464 |
% {\footnotesize\rowcolors{1}{capri!10}{white}
|
|
465 |
% \begin{tabular}{|p{4.8cm}|p{4.8cm}|}\hline
|
|
466 |
% 1 Introduction, Languages & \cellcolor{blue!50} 6 While-Language \\
|
|
467 |
% 2 Regular Expressions, Derivatives & 7 Compilation, JVM \\ |
|
468 |
% 3 Automata, Regular Languages & 8 Compiling Functional Languages \\ |
|
469 |
% 4 Lexing, Tokenising & 9 Optimisations \\ |
|
470 |
% 5 Grammars, Parsing & 10 LLVM \\ \hline |
|
471 |
% \end{tabular}%
|
|
472 |
% }; |
|
473 |
% \end{tikzpicture}
|
|
474 |
% \end{center}
|
|
| 799 | 475 |
|
| 803 | 476 |
% \end{frame}
|
477 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 799 | 478 |
|
479 |
||
480 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 531 | 481 |
% \begin{frame}[c]
|
482 |
% \small |
|
483 |
% \mbox{}\\[5mm]
|
|
484 |
% %\begin{textblock}{10}(3,5)
|
|
485 |
% \begin{tikzpicture}[scale=1.5,
|
|
486 |
% node distance=1cm, |
|
487 |
% every node/.style={minimum size=7mm}]
|
|
488 |
% \node (r1) {\bl{$r_1$}};
|
|
489 |
% \node (r2) [right=of r1] {\bl{$r_2$}};
|
|
490 |
% \draw[->,line width=1mm] (r1) -- (r2) node[above,midway] {\bl{$der\,a$}};
|
|
491 |
% \node (r3) [right=of r2] {\bl{$r_3$}};
|
|
492 |
% \draw[->,line width=1mm] (r2) -- (r3) node[above,midway] {\bl{$der\,b$}};
|
|
493 |
% \node (r4) [right=of r3] {\bl{$r_4$}};
|
|
494 |
% \draw[->,line width=1mm] (r3) -- (r4) node[above,midway] {\bl{$der\,c$}};
|
|
495 |
% \draw (r4) node[anchor=west] {\;\raisebox{3mm}{\bl{$nullable$}}};
|
|
496 |
% \node (v4) [below=of r4] {\bl{$v_4$}};
|
|
497 |
% \draw[->,line width=1mm] (r4) -- (v4); |
|
498 |
% \node (v3) [left=of v4] {\bl{$v_3$}};
|
|
499 |
% \draw[->,line width=1mm] (v4) -- (v3) node[below,midway] {\bl{$inj\,c$}};
|
|
500 |
% \node (v2) [left=of v3] {\bl{$v_2$}};
|
|
501 |
% \draw[->,line width=1mm] (v3) -- (v2) node[below,midway] {\bl{$inj\,b$}};
|
|
502 |
% \node (v1) [left=of v2] {\bl{$v_1$}};
|
|
503 |
% \draw[->,line width=1mm] (v2) -- (v1) node[below,midway] {\bl{$inj\,a$}};
|
|
504 |
% \draw[->,line width=0.5mm] (r3) -- (v3); |
|
505 |
% \draw[->,line width=0.5mm] (r2) -- (v2); |
|
506 |
% \draw[->,line width=0.5mm] (r1) -- (v1); |
|
507 |
% \draw (r4) node[anchor=north west] {\;\raisebox{-8mm}{\bl{$mkeps$}}};
|
|
508 |
% \end{tikzpicture}
|
|
509 |
% %\end{textblock}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
510 |
|
| 531 | 511 |
% \begin{center}
|
512 |
% \begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
|
513 |
% \\[-10mm] |
|
514 |
% \bl{$inj\,(c)\,c\,Empty$} & \bl{$\dn$} & \bl{$Char\,c$}\\
|
|
515 |
% \bl{$inj\,(r_1 + r_2)\,c\,Left(v)$} & \bl{$\dn$} & \bl{$Left(inj\,r_1\,c\,v)$}\\
|
|
516 |
% \bl{$inj\,(r_1 + r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Right(inj\,r_2\,c\,v)$}\\
|
|
517 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Seq(v_1,v_2)$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
518 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Left(Seq(v_1,v_2))$} & \bl{$\dn$} & \bl{$Seq(inj\,r_1\,c\,v_1,v_2)$}\\
|
|
519 |
% \bl{$inj\,(r_1 \cdot r_2)\,c\,Right(v)$} & \bl{$\dn$} & \bl{$Seq(mkeps(r_1),inj\,r_2\,c\,v)$}\\
|
|
520 |
% \bl{$inj\,(r^*)\,c\,Seq(v,vs)$} & \bl{$\dn$} & \bl{$inj\,r\,c\,v\,::\,vs$}\\
|
|
521 |
% \end{tabular}
|
|
522 |
% \end{center}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
523 |
|
| 531 | 524 |
% \end{frame}
|
525 |
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
526 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
527 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 683 | 528 |
\begin{frame}[t]
|
529 |
\frametitle{Starting Symbol}
|
|
530 |
||
531 |
\bl{\begin{plstx}[margin=1cm]
|
|
532 |
: \meta{S} ::= \meta{A}\cdot\meta{S}\cdot\meta{B} |
|
|
533 |
\meta{B}\cdot\meta{S}\cdot\meta{A} | \epsilon\\
|
|
534 |
: \meta{A} ::= a | \epsilon\\
|
|
535 |
: \meta{B} ::= b\\
|
|
536 |
\end{plstx}}
|
|
537 |
||
| 750 | 538 |
|
539 |
TODO: Testcases for math expressions |
|
540 |
\url{https://github.com/ArashPartow/math-parser-benchmark-project}
|
|
541 |
||
| 683 | 542 |
\end{frame}
|
543 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
544 |
||
545 |
||
546 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
547 |
\begin{frame}[c]
|
| 683 | 548 |
\frametitle{Hierarchy of Languages}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
549 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
550 |
Recall that languages are sets of strings. |
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
551 |
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
552 |
\begin{center}
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
553 |
\begin{tikzpicture}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
554 |
[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
555 |
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
556 |
\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
557 |
\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
558 |
\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
559 |
\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
560 |
\draw (0,-1.4) node [rect] {regular languages};
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
561 |
\end{tikzpicture}
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
562 |
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
563 |
\end{center}
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
564 |
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
565 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
566 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
567 |
|
| 531 | 568 |
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
569 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
570 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
571 |
\begin{frame}[c]
|
| 598 | 572 |
\frametitle{Parser Combinators}
|
573 |
||
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
574 |
Atomic parsers, for example |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
575 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
576 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
577 |
\bl{$1::rest \;\Rightarrow\; \{(1, rest)\}$}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
578 |
\end{center}\bigskip
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
579 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
580 |
\begin{itemize}
|
| 597 | 581 |
\item you consume one or more tokens from the\\ |
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
582 |
input (stream) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
583 |
\item also works for characters and strings |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
584 |
\end{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
585 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
586 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
587 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
588 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
589 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
590 |
|
| 686 | 591 |
Alternative parser (code \bl{$p\;|\;q$})\bigskip
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
592 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
593 |
\begin{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
594 |
\item apply \bl{$p$} and also \bl{$q$}; then combine
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
595 |
the outputs |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
596 |
\end{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
597 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
598 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
599 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
600 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
601 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
602 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
603 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
604 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
605 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
606 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
607 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
608 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
609 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
610 |
\begin{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
611 |
\item apply first \bl{$p$} producing a set of pairs
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
612 |
\item then apply \bl{$q$} to the unparsed parts
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
613 |
\item then combine the results:\medskip |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
614 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
615 |
((output$_1$, output$_2$), unparsed part) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
616 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
617 |
\end{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
618 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
619 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
620 |
\begin{tabular}{l}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
621 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
622 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
623 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
624 |
\end{tabular}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
625 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
626 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
627 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
628 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
629 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
630 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
631 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
632 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
633 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
634 |
Function parser (code \bl{$p \Rightarrow f\;$})\bigskip
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
635 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
636 |
\begin{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
637 |
\item apply \bl{$p$} producing a set of pairs
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
638 |
\item then apply the function \bl{$f$} to each first component
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
639 |
\end{itemize}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
640 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
641 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
642 |
\begin{tabular}{l}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
643 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
644 |
\end{tabular}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
645 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
646 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
647 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
648 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
649 |
|
| 531 | 650 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
651 |
\begin{frame}[c]
|
|
652 |
\frametitle{Types of Parsers}
|
|
653 |
||
654 |
\begin{itemize}
|
|
655 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
|
656 |
then \bl{$p \sim q$} returns results of type
|
|
657 |
||
658 |
\begin{center}
|
|
659 |
\bl{$T \times S$}
|
|
660 |
\end{center}\pause
|
|
661 |
||
662 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
|
| 686 | 663 |
and \bl{$p \;|\; q$} returns results of type
|
| 531 | 664 |
|
665 |
\begin{center}
|
|
666 |
\bl{$T$}
|
|
667 |
\end{center}\pause
|
|
668 |
||
669 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
|
670 |
\bl{$T$} to \bl{$S$}, then
|
|
671 |
\bl{$p \Rightarrow f$} returns results of type
|
|
672 |
||
673 |
\begin{center}
|
|
674 |
\bl{$S$}
|
|
675 |
\end{center}
|
|
676 |
||
677 |
\end{itemize}
|
|
678 |
||
679 |
\end{frame}
|
|
680 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
681 |
||
682 |
||
683 |
||
684 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
685 |
\begin{frame}[c]
|
|
686 |
\frametitle{Two Grammars}
|
|
687 |
||
688 |
Which languages are recognised by the following two grammars? |
|
689 |
||
| 597 | 690 |
\bl{\begin{plstx}[margin=3cm]
|
691 |
: \meta{S} ::= \liningnums{1}\cdot\meta{S}\cdot \meta{S} | \epsilon\\
|
|
692 |
\end{plstx}}
|
|
| 531 | 693 |
|
| 597 | 694 |
\bl{\begin{plstx}[margin=3cm]
|
695 |
: \meta{U} ::= \liningnums{1}\cdot\meta{U} | \epsilon\\
|
|
696 |
\end{plstx}}
|
|
| 531 | 697 |
|
698 |
\end{frame}
|
|
699 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
700 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
701 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
702 |
\begin{frame}[t]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
703 |
\frametitle{Ambiguous Grammars}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
704 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
705 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
706 |
\begin{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
707 |
\begin{axis}[xlabel={\pcode{1}s},ylabel={time in secs},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
708 |
enlargelimits=false, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
709 |
xtick={0,100,...,1000},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
710 |
xmax=1050, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
711 |
ymax=33, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
712 |
ytick={0,5,...,30},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
713 |
scaled ticks=false, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
714 |
axis lines=left, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
715 |
width=11cm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
716 |
height=7cm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
717 |
legend entries={unambiguous,ambiguous},
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
718 |
legend pos=north east, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
719 |
legend cell align=left, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
720 |
x tick label style={font=\small,/pgf/number format/1000 sep={}}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
721 |
\addplot[blue,mark=*, mark options={fill=white}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
722 |
table {s-grammar1.data};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
723 |
\only<2>{
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
724 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
725 |
table {s-grammar2.data};}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
726 |
\end{axis}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
727 |
\end{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
728 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
729 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
730 |
\end{frame}
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
731 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
732 |
|
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
733 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
734 |
\begin{frame}[c]
|
| 597 | 735 |
\frametitle{Arithmetic Expressions}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
736 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
737 |
A grammar for arithmetic expressions and numbers: |
| 50 | 738 |
|
| 597 | 739 |
\bl{\begin{plstx}[margin=1cm]
|
740 |
: \meta{E} ::= \meta{E} \cdot + \cdot \meta{E}
|
|
741 |
| \meta{E} \cdot * \cdot \meta{E}
|
|
742 |
| ( \cdot \meta{E} \cdot ) | \meta{N}\\
|
|
743 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
744 |
0 | 1 | \ldots | 9\\ |
|
745 |
\end{plstx}}
|
|
| 49 | 746 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
747 |
Unfortunately it is left-recursive (and ambiguous).\medskip\\ |
| 597 | 748 |
A problem for \alert{recursive descent parsers} (e.g.~parser
|
749 |
combinators). \bigskip\pause |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
750 |
|
| 597 | 751 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
752 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
753 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
754 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
755 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
756 |
\begin{frame}[t]
|
| 597 | 757 |
\frametitle{Numbers}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
758 |
|
| 597 | 759 |
\bl{\begin{plstx}[margin=1cm]
|
760 |
: \meta{N} ::= \meta{N} \cdot \meta{N} |
|
|
761 |
0 | 1 | \ldots | 9\\ |
|
762 |
\end{plstx}}
|
|
| 49 | 763 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
764 |
A non-left-recursive, non-ambiguous grammar for numbers: |
| 49 | 765 |
|
| 597 | 766 |
\bl{\begin{plstx}[margin=1cm]
|
767 |
: \meta{N} ::= 0 \cdot \meta{N} | 1 \cdot \meta{N} | \ldots |
|
|
768 |
0 | 1 | \ldots | 9\\ |
|
769 |
\end{plstx}}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
770 |
|
| 597 | 771 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
772 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
773 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
774 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
775 |
\begin{frame}[c]
|
| 597 | 776 |
\frametitle{Removing Left-Recursion}
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
777 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
778 |
The rule for numbers is directly left-recursive: |
| 49 | 779 |
|
780 |
\begin{center}
|
|
| 50 | 781 |
\bl{\begin{tabular}{lcl}
|
| 597 | 782 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \meta{N} \;|\; 0 \;|\; 1\;\;\;\;(\ldots)$
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
783 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
784 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
785 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
786 |
Translate |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
787 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
788 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
789 |
\begin{tabular}{ccc}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
790 |
\bl{\begin{tabular}{lcl}
|
| 597 | 791 |
$\meta{N}$ & $::=$ & $\meta{N} \cdot \alpha$\\
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
792 |
& $\;|\;$ & $\beta$\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
793 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
794 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
795 |
& {\Large$\Rightarrow$} &
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
796 |
\bl{\begin{tabular}{lcl}
|
| 597 | 797 |
$\meta{N}$ & $::=$ & $\beta \cdot \meta{N}'$\\
|
798 |
$\meta{N}'$ & $::=$ & $\alpha \cdot \meta{N}'$\\
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
799 |
& $\;|\;$ & $\epsilon$ |
| 50 | 800 |
\end{tabular}}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
801 |
\end{tabular}
|
| 50 | 802 |
\end{center}\pause
|
803 |
||
| 597 | 804 |
Which means in this case: |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
805 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
806 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
807 |
\bl{\begin{tabular}{lcl}
|
| 597 | 808 |
$\meta{N}$ & $\rightarrow$ & $0 \cdot \meta{N}' \;|\; 1 \cdot \meta{N}'$\\
|
809 |
$\meta{N}'$ & $\rightarrow$ & $\meta{N} \cdot \meta{N}' \;|\; \epsilon$\\
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
810 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
811 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
812 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
813 |
|
| 597 | 814 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
815 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
816 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
817 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 685 | 818 |
%\begin{frame}[c]
|
819 |
%\frametitle{Operator Precedences}
|
|
820 |
% |
|
821 |
% |
|
822 |
%To disambiguate |
|
823 |
% |
|
824 |
%\begin{center}
|
|
825 |
%\bl{\begin{tabular}{lcl}
|
|
826 |
%$\meta{E}$ & $::=$ & $\meta{E} \cdot + \cdot \meta{E} \;|\;\meta{E} \cdot * \cdot \meta{E} \;|\;( \cdot \meta{E} \cdot ) \;|\;\meta{N}$ \\
|
|
827 |
%\end{tabular}}
|
|
828 |
%\end{center}
|
|
829 |
% |
|
830 |
%Decide on how many precedence levels, say\medskip\\ |
|
831 |
%highest for \bl{$()$}, medium for \bl{*}, lowest for \bl{+}
|
|
832 |
% |
|
833 |
%\begin{center}
|
|
834 |
%\bl{\begin{tabular}{lcl}
|
|
835 |
%$\meta{E}_{low}$ & $::=$ & $\meta{E}_{med} \cdot + \cdot \meta{E}_{low} \;|\; \meta{E}_{med}$ \\
|
|
836 |
%$\meta{E}_{med}$ & $::=$ & $\meta{E}_{hi} \cdot * \cdot \meta{E}_{med} \;|\; \meta{E}_{hi}$\\
|
|
837 |
%$\meta{E}_{hi}$ & $::=$ & $( \cdot \meta{E}_{low} \cdot ) \;|\;\meta{N}$ \\
|
|
838 |
%\end{tabular}}
|
|
839 |
%\end{center}\pause
|
|
840 |
% |
|
841 |
%\small What happens with \bl{$1 + 3 + 4$}?
|
|
842 |
%\end{frame}
|
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
843 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
844 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
845 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
846 |
\begin{frame}[c]
|
| 597 | 847 |
\frametitle{Chomsky Normal Form}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
848 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
849 |
All rules must be of the form |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
850 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
851 |
\begin{center}
|
| 597 | 852 |
\bl{$\meta{A} ::= a$}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
853 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
854 |
|
| 50 | 855 |
or |
856 |
||
857 |
\begin{center}
|
|
| 597 | 858 |
\bl{$\meta{A} ::= \meta{B}\cdot \meta{C}$}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
859 |
\end{center}
|
| 49 | 860 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
861 |
No rule can contain \bl{$\epsilon$}.
|
| 49 | 862 |
|
| 597 | 863 |
\end{frame}
|
| 49 | 864 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
865 |
||
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
866 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
867 |
\begin{frame}[c]
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
868 |
\frametitle{\begin{tabular}{c}$\epsilon$-Removal\end{tabular}}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
869 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
870 |
\begin{enumerate}
|
| 597 | 871 |
\item If \bl{$A::= \alpha \cdot B \cdot \beta$} and \bl{$B ::= \epsilon$} are in the grammar,
|
872 |
then add \bl{$A::= \alpha \cdot \beta$} (iterate if necessary).
|
|
873 |
\item Throw out all \bl{$B ::= \epsilon$}.
|
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
874 |
\end{enumerate}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
875 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
876 |
\small |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
877 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
878 |
\begin{tabular}{ccc}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
879 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
| 597 | 880 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'$\\ |
881 |
$N'$ & $::=$ & $N \cdot N'\;|\;\epsilon$\\ |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
882 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
883 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
884 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
885 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
886 |
\\ |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
887 |
\end{tabular}} &
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
888 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
889 |
\\ |
| 597 | 890 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ |
891 |
$N'$ & $::=$ & $N \cdot N'\;|\;N\;|\;\epsilon$\\ |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
892 |
\\ |
| 597 | 893 |
$N$ & $::=$ & $0 \cdot N' \;|\; 1\cdot N'\;|\;0\;|\;1$\\ |
894 |
$N'$ & $::=$ & $N \cdot N'\;|\;N$\\ |
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
895 |
\end{tabular}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
896 |
\end{tabular}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
897 |
\end{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
898 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
899 |
\pause\normalsize |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
900 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
901 |
\bl{\begin{tabular}{l@{\hspace{1mm}}c@{\hspace{1mm}}l}
|
| 597 | 902 |
$N$ & $::=$ & $0 \cdot N\;|\; 1\cdot N\;|\;0\;|\;1$\\ |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
903 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
904 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
905 |
\end{center}
|
|
368
a9911966c0df
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
366
diff
changeset
|
906 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
907 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
908 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
909 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
910 |
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
911 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
912 |
\begin{frame}[c]
|
| 597 | 913 |
\frametitle{CYK Algorithm}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
914 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
915 |
If grammar is in Chomsky normalform \ldots |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
916 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
917 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
918 |
\bl{\begin{tabular}{@ {}lcl@ {}}
|
| 597 | 919 |
$\meta{S}$ & $::=$ & $\meta{N}\cdot \meta{P}$ \\
|
920 |
$\meta{P}$ & $::=$ & $\meta{V}\cdot \meta{N}$ \\
|
|
921 |
$\meta{N}$ & $::=$ & $\meta{N}\cdot \meta{N}$ \\
|
|
922 |
$\meta{N}$ & $::=$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
|
|
923 |
$\meta{V}$ & $::=$ & $\texttt{trains}$
|
|
| 49 | 924 |
\end{tabular}}
|
925 |
\end{center}
|
|
926 |
||
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
927 |
\bl{\texttt{Jeff trains geometry students}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
928 |
|
| 597 | 929 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
930 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 597 | 931 |
|
932 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
933 |
\begin{frame}[c]
|
| 597 | 934 |
\frametitle{CYK Algorithm}
|
| 49 | 935 |
|
936 |
||
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
937 |
\begin{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
938 |
\item fastest possible algorithm for recognition problem |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
939 |
\item runtime is \bl{$O(n^3)$}\bigskip
|
| 597 | 940 |
\item grammars need to be transformed into CNF |
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
941 |
\end{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
942 |
|
| 597 | 943 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
944 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
945 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
946 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
947 |
\begin{frame}[c]
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
948 |
\frametitle{The Goal of this Course}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
949 |
\mbox{}\\[-26mm]\mbox{}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
950 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
951 |
\begin{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
952 |
\begin{tikzpicture}[scale=1,
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
953 |
node/.style={
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
954 |
rectangle,rounded corners=3mm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
955 |
very thick,draw=black!50, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
956 |
minimum height=18mm, minimum width=20mm, |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
957 |
top color=white,bottom color=black!20}] |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
958 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
959 |
\node at (3.05, 1.8) {\Large\bf Write a Compiler};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
960 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
961 |
\node (0) at (-2.3,0) {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
962 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
963 |
\node (A) at (0,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
964 |
\node [below right] at (A.north west) {lexer};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
965 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
966 |
\node (B) at (3,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
967 |
\node [below right=1mm] at (B.north west) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
968 |
{\mbox{}\hspace{-1mm}parser};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
969 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
970 |
\node (C) at (6,0) [node] {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
971 |
\node [below right] at (C.north west) |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
972 |
{\mbox{}\hspace{-1mm}code gen};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
973 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
974 |
\node (1) at (8.4,0) {};
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
975 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
976 |
\draw [->,line width=4mm] (0) -- (A); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
977 |
\draw [->,line width=4mm] (A) -- (B); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
978 |
\draw [->,line width=4mm] (B) -- (C); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
979 |
\draw [->,line width=4mm] (C) -- (1); |
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
980 |
\end{tikzpicture}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
981 |
\end{center}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
982 |
|
| 598 | 983 |
We have a lexer and a parser\ldots |
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
984 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
985 |
\end{frame}
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
986 |
|
|
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
987 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
988 |
\begin{frame}[c]
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
989 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
990 |
\begin{center}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
991 |
\bl{\begin{tabular}{@{}lcl@{}}
|
| 598 | 992 |
\meta{Stmt} & $::=$ & $\texttt{skip}$\\
|
993 |
& $|$ & \textit{Id}\;\texttt{:=}\;\meta{AExp}\\
|
|
994 |
& $|$ & \texttt{if}\; \meta{BExp} \;\texttt{then}\; \meta{Block} \;\texttt{else}\; \meta{Block}\\
|
|
995 |
& $|$ & \texttt{while}\; \meta{BExp} \;\texttt{do}\; \meta{Block}\\
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
996 |
& $|$ & \texttt{read}\;\textit{Id}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
997 |
& $|$ & \texttt{write}\;\textit{Id}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
998 |
& $|$ & \texttt{write}\;\textit{String}\medskip\\
|
| 598 | 999 |
\meta{Stmts} & $::=$ & \meta{Stmt} \;\texttt{;}\; \meta{Stmts}\\
|
1000 |
& $|$ & \meta{Stmt}\medskip\\
|
|
1001 |
\meta{Block} & $::=$ & \texttt{\{}\,\meta{Stmts}\,\texttt{\}}\\
|
|
1002 |
& $|$ & \meta{Stmt}\medskip\\
|
|
1003 |
\meta{AExp} & $::=$ & \ldots\\
|
|
1004 |
\meta{BExp} & $::=$ & \ldots\\
|
|
| 50 | 1005 |
\end{tabular}}
|
1006 |
\end{center}
|
|
|
366
5a83336a9690
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
365
diff
changeset
|
1007 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1008 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1009 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1010 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1011 |
\mode<presentation>{
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1012 |
\begin{frame}[c]
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1013 |
|
| 744 | 1014 |
??%%\mbox{\lstinputlisting[language=while]{../progs/fib.while}}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1015 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1016 |
\end{frame}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1017 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1018 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1019 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1020 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1021 |
\begin{frame}[c]
|
| 598 | 1022 |
\frametitle{An Interpreter}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1023 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1024 |
\begin{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1025 |
\bl{\begin{tabular}{l}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1026 |
$\{$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1027 |
\;\;$x := 5 \text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1028 |
\;\;$y := x * 3\text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1029 |
\;\;$y := x * 4\text{;}$\\
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1030 |
\;\;$x := u * 3$\\ |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1031 |
$\}$ |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1032 |
\end{tabular}}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1033 |
\end{center}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1034 |
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1035 |
\begin{itemize}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1036 |
\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1037 |
\item \bl{\text{eval}(stmt, env)}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1038 |
\end{itemize}
|
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1039 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1040 |
|
| 598 | 1041 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1042 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1043 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1044 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1045 |
\begin{frame}[c]
|
| 598 | 1046 |
\frametitle{An Interpreter}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1047 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1048 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1049 |
\bl{\begin{tabular}{@{}lcl@{}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1050 |
$\text{eval}(n, E)$ & $\dn$ & $n$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1051 |
$\text{eval}(x, E)$ & $\dn$ & $E(x)$ \;\;\;\textcolor{black}{lookup \bl{$x$} in \bl{$E$}}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1052 |
$\text{eval}(a_1 + a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) + \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1053 |
$\text{eval}(a_1 - a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) - \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1054 |
$\text{eval}(a_1 * a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) * \text{eval}(a_2, E)$\bigskip\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1055 |
$\text{eval}(a_1 = a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) = \text{eval}(a_2, E)$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1056 |
$\text{eval}(a_1\,!\!= a_2, E)$ & $\dn$ & $\neg(\text{eval}(a_1, E) = \text{eval}(a_2, E))$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1057 |
$\text{eval}(a_1 < a_2, E)$ & $\dn$ & $\text{eval}(a_1, E) < \text{eval}(a_2, E)$\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1058 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1059 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1060 |
|
| 598 | 1061 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1062 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 598 | 1063 |
|
1064 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1065 |
\begin{frame}[c]
|
| 598 | 1066 |
\frametitle{An Interpreter (2)}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1067 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1068 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1069 |
\bl{\begin{tabular}{@{}lcl@{}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1070 |
$\text{eval}(\text{skip}, E)$ & $\dn$ & $E$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1071 |
$\text{eval}(x:=a, E)$ & $\dn$ & \bl{$E(x \mapsto \text{eval}(a, E))$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1072 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{if}\;b\;\text{then}\;cs_1\;\text{else}\;cs_2 , E) \dn$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1073 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)\;\text{then}\;
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1074 |
\text{eval}(cs_1,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1075 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\phantom{\text{if}\;\text{eval}(b,E)\;}\text{else}\;\text{eval}(cs_2,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1076 |
\multicolumn{3}{@{}l@{}}{$\text{eval}(\text{while}\;b\;\text{do}\;cs, E) \dn$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1077 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{if}\;\text{eval}(b,E)$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1078 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{then}\;
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1079 |
\text{eval}(\text{while}\;b\;\text{do}\;cs, \text{eval}(cs,E))$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1080 |
\multicolumn{3}{@{}l@{}}{\hspace{2cm}$\text{else}\; E$}\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1081 |
$\text{eval}(\text{write}\; x, E)$ & $\dn$ & $\{\;\text{println}(E(x))\; ;\;E\;\}$\\
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1082 |
\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1083 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1084 |
|
| 598 | 1085 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1086 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1087 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1088 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1089 |
\begin{frame}[c]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1090 |
\frametitle{\begin{tabular}{c}Test Program\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1091 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1092 |
\mbox{}\\[-18mm]\mbox{}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1093 |
|
| 744 | 1094 |
?? |
1095 |
%{\lstset{language=While}%%\fontsize{10}{12}\selectfont
|
|
1096 |
%\texttt{\lstinputlisting{../progs/loops.while}}}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1097 |
|
|
295
19f23c4c2167
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
215
diff
changeset
|
1098 |
\end{frame}
|
|
169
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1099 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
57df3d7b4a25
added slides
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
168
diff
changeset
|
1100 |
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1101 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1102 |
\mode<presentation>{
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1103 |
\begin{frame}[t]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1104 |
\frametitle{\begin{tabular}{c}Interpreted Code\end{tabular}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1105 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1106 |
\begin{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1107 |
\begin{tikzpicture}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1108 |
\begin{axis}[axis x line=bottom, axis y line=left, xlabel=n, ylabel=secs, legend style=small]
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1109 |
\addplot+[smooth] file {interpreted.data};
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1110 |
\end{axis}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1111 |
\end{tikzpicture}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1112 |
\end{center}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1113 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1114 |
\end{frame}}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1115 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1116 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1117 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1118 |
\begin{frame}[c]
|
| 685 | 1119 |
\frametitle{Java Virtual Machine}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1120 |
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1121 |
\begin{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1122 |
\item introduced in 1995 |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1123 |
\item is a stack-based VM (like Postscript, CLR of .Net) |
| 685 | 1124 |
\item contains a JIT compiler\\ |
1125 |
\begin{itemize}
|
|
1126 |
\item From the Cradle to the Holy Graal - the JDK Story |
|
1127 |
\item \url{https://www.youtube.com/watch?v=h419kfbLhUI}
|
|
1128 |
\end{itemize}
|
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1129 |
\item is garbage collected $\Rightarrow$ no buffer overflows |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1130 |
\item some languages compile to the JVM: Scala, Clojure\ldots |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1131 |
\end{itemize}
|
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1132 |
|
| 685 | 1133 |
\end{frame}
|
|
365
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1134 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
9b71dead1219
updated
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
295
diff
changeset
|
1135 |
|
| 685 | 1136 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
1137 |
\begin{frame}[c]
|
|
1138 |
\frametitle{LLVM}
|
|
1139 |
||
1140 |
\begin{itemize}
|
|
1141 |
\item LLVM started by academics in 2000 (University of Illinois in |
|
1142 |
Urbana-Champaign) |
|
1143 |
\item suite of compiler tools |
|
1144 |
\item SSA-based intermediate language |
|
1145 |
\item no need to allocate registers |
|
| 686 | 1146 |
\item source languages: C, C++, Rust, Go, Swift |
1147 |
\item target CPUs: x86, ARM, PowerPC, \ldots |
|
| 685 | 1148 |
\end{itemize}
|
1149 |
\end{frame}
|
|
1150 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 702 | 1151 |
|
| 598 | 1152 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 666 | 1153 |
%\begin{frame}[c]
|
1154 |
% \frametitle{Coursework: MkEps}
|
|
1155 |
% |
|
1156 |
%\begin{center}
|
|
1157 |
%\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
|
1158 |
% \bl{$mkeps([c_1 c_2 \ldots c_n])$} & \bl{$\dn$} & $\bl{undefined}$\\
|
|
1159 |
% \bl{$mkeps(r^*)$} & \bl{$\dn$} & $\bl{Stars\,[]}$\\
|
|
1160 |
% \bl{$mkeps(r^{\{n\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\\
|
|
1161 |
% \bl{$mkeps(r^{\{n..\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\\
|
|
1162 |
% \bl{$mkeps(r^{\{..n\}})$} & \bl{$\dn$} & $\bl{Stars\,[]}$\\
|
|
1163 |
% \bl{$mkeps(r^{\{n..m\}})$} & \bl{$\dn$} & $\bl{Stars\,(mkeps(r))^n}$\medskip\\
|
|
1164 |
% |
|
1165 |
% \bl{$mkeps(r^+)$} & \bl{$\dn$} & \bl{$mkeps(r^{\{1..\}})$}\\
|
|
1166 |
% \bl{$mkeps(r^?)$} & \bl{$\dn$} & \bl{$mkeps(r^{\{..1\}})$}\\
|
|
1167 |
%\end{tabular}
|
|
1168 |
%\end{center}
|
|
1169 |
% |
|
1170 |
%\end{frame}
|
|
1171 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1172 |
% |
|
1173 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1174 |
%\begin{frame}[c]
|
|
1175 |
% \frametitle{Coursework: Inj}
|
|
1176 |
% |
|
1177 |
%\begin{center}
|
|
1178 |
%\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
|
|
1179 |
% \bl{$inj([c_1 c_2 \ldots c_n])\,c\,Empty$} & \bl{$\dn$} & $\bl{Chr\,c}$\\
|
|
1180 |
% \bl{$inj(r^*)\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
1181 |
% \bl{$inj(r^{\{n\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
1182 |
% \bl{$inj(r^{\{n..\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
1183 |
% \bl{$inj(r^{\{..n\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\\
|
|
1184 |
% \bl{$inj(r^{\{n..m\}})\,c\;(Seq\,v\,(Stars\,vs))$} & \bl{$\dn$} & $\bl{Stars\,(inj\,r\,c\,v::vs)}$\medskip\\
|
|
1185 |
% |
|
1186 |
% \bl{$inj(r^+)\,c\,v$} & \bl{$\dn$} & \bl{$inj(r^{\{1..\}})\,c\,v$}\\
|
|
1187 |
% \bl{$inj(r^?)\,c\,v$} & \bl{$\dn$} & \bl{$inj(r^{\{..1\}})\,c\,v$}\\
|
|
1188 |
%\end{tabular}
|
|
1189 |
%\end{center}
|
|
1190 |
% |
|
1191 |
%\end{frame}
|
|
1192 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
| 702 | 1193 |
% |
| 598 | 1194 |
|
| 809 | 1195 |
|
1196 |
||
1197 |
||
| 49 | 1198 |
\end{document}
|
1199 |
||
| 803 | 1200 |
|
1201 |
||
1202 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1203 |
\begin{frame}[c]
|
|
1204 |
\frametitle{Parser Combinators}
|
|
1205 |
||
1206 |
Parser combinators: \bigskip |
|
1207 |
||
1208 |
\begin{minipage}{1.1\textwidth}
|
|
1209 |
\begin{center}
|
|
1210 |
\mbox{}\hspace{-12mm}\mbox{}$\underbrace{\text{list of tokens}}_{\text{input}}$ \bl{$\Rightarrow$}
|
|
1211 |
$\underbrace{\text{set of (parsed input, unparsed input)}}_{\text{output}}$
|
|
1212 |
\end{center}
|
|
1213 |
\end{minipage}\bigskip
|
|
1214 |
||
1215 |
\begin{itemize}
|
|
1216 |
\item atomic parsers |
|
1217 |
\item sequencing |
|
1218 |
\item alternative |
|
1219 |
\item semantic action (map-parser) |
|
1220 |
\end{itemize}
|
|
1221 |
||
1222 |
\end{frame}
|
|
1223 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1224 |
||
1225 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1226 |
\begin{frame}[c]
|
|
1227 |
||
1228 |
Atomic parsers, for example, number tokens |
|
1229 |
||
1230 |
\begin{center}
|
|
1231 |
\bl{$\texttt{Num(123)}::rest \;\Rightarrow\; \{(\texttt{Num(123)}, rest)\}$}
|
|
1232 |
\end{center}\bigskip
|
|
1233 |
||
1234 |
\begin{itemize}
|
|
1235 |
\item you consume one or more token from the\\ |
|
1236 |
input (stream) |
|
1237 |
\item also works for characters and strings |
|
1238 |
\end{itemize}
|
|
1239 |
\end{frame}
|
|
1240 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1241 |
||
1242 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1243 |
\begin{frame}[c]
|
|
1244 |
||
1245 |
Alternative parser (code \bl{$p\;||\;q$})\bigskip
|
|
1246 |
||
1247 |
\begin{itemize}
|
|
1248 |
\item apply \bl{$p$} and also \bl{$q$}; then combine
|
|
1249 |
the outputs |
|
1250 |
\end{itemize}
|
|
1251 |
||
1252 |
\begin{center}
|
|
1253 |
\large \bl{$p(\text{input}) \cup q(\text{input})$}
|
|
1254 |
\end{center}
|
|
1255 |
||
1256 |
\end{frame}
|
|
1257 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1258 |
||
1259 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1260 |
\begin{frame}[c]
|
|
1261 |
||
1262 |
Sequence parser (code \bl{$p\sim q$})\bigskip
|
|
1263 |
||
1264 |
\begin{itemize}
|
|
1265 |
\item apply first \bl{$p$} producing a set of pairs
|
|
1266 |
\item then apply \bl{$q$} to the unparsed part
|
|
1267 |
\item then combine the results:\medskip |
|
1268 |
\begin{center}
|
|
1269 |
((output$_1$, output$_2$), unparsed part) |
|
1270 |
\end{center}
|
|
1271 |
\end{itemize}
|
|
1272 |
||
1273 |
\begin{center}
|
|
1274 |
\begin{tabular}{l}
|
|
1275 |
\large \bl{$\{((o_1, o_2), u_2) \;|\;$}\\[2mm]
|
|
1276 |
\large\mbox{}\hspace{15mm} \bl{$(o_1, u_1) \in p(\text{input}) \wedge$}\\[2mm]
|
|
1277 |
\large\mbox{}\hspace{15mm} \bl{$(o_2, u_2) \in q(u_1)\}$}
|
|
1278 |
\end{tabular}
|
|
1279 |
\end{center}
|
|
1280 |
||
1281 |
||
1282 |
\end{frame}
|
|
1283 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1284 |
||
1285 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1286 |
\begin{frame}[c]
|
|
1287 |
||
1288 |
Map-parser (code \bl{$p.map(f)\;$})\bigskip
|
|
1289 |
||
1290 |
\begin{itemize}
|
|
1291 |
\item apply \bl{$p$} producing a set of pairs
|
|
1292 |
\item then apply the function \bl{$f$} to each first component
|
|
1293 |
\end{itemize}
|
|
1294 |
||
1295 |
\begin{center}
|
|
1296 |
\begin{tabular}{l}
|
|
1297 |
\large \bl{$\{(f(o_1), u_1) \;|\; (o_1, u_1) \in p(\text{input})\}$}
|
|
1298 |
\end{tabular}
|
|
1299 |
\end{center}\bigskip\bigskip\pause
|
|
1300 |
||
1301 |
\bl{$f$} is the semantic action (``what to do with the parsed input'')
|
|
1302 |
||
1303 |
\end{frame}
|
|
1304 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1305 |
||
1306 |
||
1307 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1308 |
\mode<presentation>{
|
|
1309 |
\begin{frame}[c]
|
|
1310 |
\frametitle{\begin{tabular}{c}Semantic Actions\end{tabular}}
|
|
1311 |
||
1312 |
Addition |
|
1313 |
||
1314 |
\begin{center}
|
|
1315 |
\bl{$\meta{T} \sim + \sim \meta{E} \Rightarrow \underbrace{f\,((x,y), z) \Rightarrow x + z}_{\text{semantic action}}$}
|
|
1316 |
\end{center}\pause
|
|
1317 |
||
1318 |
Multiplication |
|
1319 |
||
1320 |
\begin{center}
|
|
1321 |
\bl{$\meta{F} \sim * \sim \meta{T} \Rightarrow f\,((x,y), z) \Rightarrow x * z$}
|
|
1322 |
\end{center}\pause
|
|
1323 |
||
1324 |
Parenthesis |
|
1325 |
||
1326 |
\begin{center}
|
|
1327 |
\bl{$\text{(} \sim \meta{E} \sim \text{)} \Rightarrow f\,((x,y), z) \Rightarrow y$}
|
|
1328 |
\end{center}
|
|
1329 |
||
1330 |
\end{frame}}
|
|
1331 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1332 |
||
1333 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1334 |
\begin{frame}[c]
|
|
1335 |
\frametitle{Types of Parsers}
|
|
1336 |
||
1337 |
\begin{itemize}
|
|
1338 |
\item {\bf Sequencing}: if \bl{$p$} returns results of type \bl{$T$}, and \bl{$q$} results of type \bl{$S$},
|
|
1339 |
then \bl{$p \sim q$} returns results of type
|
|
1340 |
||
1341 |
\begin{center}
|
|
1342 |
\bl{$T \times S$}
|
|
1343 |
\end{center}\pause
|
|
1344 |
||
1345 |
\item {\bf Alternative}: if \bl{$p$} returns results of type \bl{$T$} then \bl{$q$} \alert{must} also have results of type \bl{$T$},
|
|
1346 |
and \bl{$p \;||\; q$} returns results of type
|
|
1347 |
||
1348 |
\begin{center}
|
|
1349 |
\bl{$T$}
|
|
1350 |
\end{center}\pause
|
|
1351 |
||
1352 |
\item {\bf Semantic Action}: if \bl{$p$} returns results of type \bl{$T$} and \bl{$f$} is a function from
|
|
1353 |
\bl{$T$} to \bl{$S$}, then
|
|
1354 |
\bl{$p \Rightarrow f$} returns results of type
|
|
1355 |
||
1356 |
\begin{center}
|
|
1357 |
\bl{$S$}
|
|
1358 |
\end{center}
|
|
1359 |
||
1360 |
\end{itemize}
|
|
1361 |
||
1362 |
\end{frame}
|
|
1363 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1364 |
||
1365 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1366 |
\begin{frame}[c]
|
|
1367 |
\frametitle{Input Types of Parsers}
|
|
1368 |
||
1369 |
\begin{itemize}
|
|
1370 |
\item input: \alert{token list}
|
|
1371 |
\item output: set of (output\_type, \alert{token list})
|
|
1372 |
\end{itemize}\bigskip\pause
|
|
1373 |
||
1374 |
actually it can be any input type as long as it is a kind of |
|
1375 |
sequence (for example a string) |
|
1376 |
||
1377 |
\end{frame}
|
|
1378 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1379 |
||
1380 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1381 |
\begin{frame}[c]
|
|
1382 |
\frametitle{Scannerless Parsers}
|
|
1383 |
||
1384 |
\begin{itemize}
|
|
1385 |
\item input: \alert{string}
|
|
1386 |
\item output: set of (output\_type, \alert{string})
|
|
1387 |
\end{itemize}\bigskip\bigskip
|
|
1388 |
||
1389 |
but using lexers is better because whitespaces or comments can be |
|
1390 |
filtered out; then input is a sequence of tokens |
|
1391 |
||
1392 |
\end{frame}
|
|
1393 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1394 |
||
1395 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1396 |
\begin{frame}[c]
|
|
1397 |
\frametitle{Successful Parses}
|
|
1398 |
||
1399 |
\begin{itemize}
|
|
1400 |
\item input: string |
|
1401 |
\item output: \alert{set of} (output\_type, string)
|
|
1402 |
\end{itemize}\bigskip
|
|
1403 |
||
1404 |
a parse is successful whenever the input has been fully |
|
1405 |
``consumed'' (that is the second component is empty) |
|
1406 |
||
1407 |
\end{frame}
|
|
1408 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1409 |
||
1410 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1411 |
\begin{frame}[c]
|
|
1412 |
\frametitle{Abstract Parser Class}
|
|
1413 |
||
1414 |
\small |
|
1415 |
\lstinputlisting[language=Scala,xleftmargin=1mm] |
|
1416 |
{../progs/app7.scala}
|
|
1417 |
\end{frame}
|
|
1418 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1419 |
||
1420 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1421 |
\begin{frame}[c]
|
|
1422 |
||
1423 |
\small |
|
1424 |
\fontsize{10}{12}\selectfont
|
|
1425 |
\lstinputlisting[language=Scala,xleftmargin=1mm] |
|
1426 |
{../progs/app8.scala}
|
|
1427 |
\end{frame}
|
|
1428 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1429 |
||
1430 |
||
1431 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1432 |
\begin{frame}[c]
|
|
1433 |
\frametitle{Two Grammars}
|
|
1434 |
||
1435 |
Which languages are recognised by the following two grammars? |
|
1436 |
||
1437 |
\begin{center}
|
|
1438 |
\bl{\begin{tabular}{lcl}
|
|
1439 |
$\meta{S}$ & $\rightarrow$ & $1 \cdot \meta{S} \cdot \meta{S}$\\
|
|
1440 |
& $|$ & $\epsilon$ |
|
1441 |
\end{tabular}}
|
|
1442 |
\end{center}\bigskip
|
|
1443 |
||
1444 |
\begin{center}
|
|
1445 |
\bl{\begin{tabular}{lcl}
|
|
1446 |
$\meta{U}$ & $\rightarrow$ & $1 \cdot \meta{U}$\\
|
|
1447 |
& $|$ & $\epsilon$ |
|
1448 |
\end{tabular}}
|
|
1449 |
\end{center}
|
|
1450 |
||
1451 |
\end{frame}
|
|
1452 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1453 |
||
1454 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1455 |
\begin{frame}[t]
|
|
1456 |
\frametitle{Ambiguous Grammars}
|
|
1457 |
||
1458 |
\begin{center}
|
|
1459 |
\begin{tikzpicture}
|
|
1460 |
\begin{axis}[xlabel={\pcode{1}s},ylabel={time in secs},
|
|
1461 |
enlargelimits=false, |
|
1462 |
xtick={0,100,...,1000},
|
|
1463 |
xmax=1050, |
|
1464 |
ymax=33, |
|
1465 |
ytick={0,5,...,30},
|
|
1466 |
scaled ticks=false, |
|
1467 |
axis lines=left, |
|
1468 |
width=11cm, |
|
1469 |
height=7cm, |
|
1470 |
legend entries={unambiguous,ambiguous},
|
|
1471 |
legend pos=north east, |
|
1472 |
legend cell align=left, |
|
1473 |
x tick label style={font=\small,/pgf/number format/1000 sep={}}]
|
|
1474 |
\addplot[blue,mark=*, mark options={fill=white}]
|
|
1475 |
table {s-grammar1.data};
|
|
1476 |
\only<2>{
|
|
1477 |
\addplot[red,mark=triangle*, mark options={fill=white}]
|
|
1478 |
table {s-grammar2.data};}
|
|
1479 |
\end{axis}
|
|
1480 |
\end{tikzpicture}
|
|
1481 |
\end{center}
|
|
1482 |
||
1483 |
\end{frame}
|
|
1484 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
1485 |
||
| 809 | 1486 |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
1487 |
||
| 803 | 1488 |
|
1489 |
||
1490 |
||
| 49 | 1491 |
%%% Local Variables: |
1492 |
%%% mode: latex |
|
1493 |
%%% TeX-master: t |
|
1494 |
%%% End: |
|
1495 |